Two moles of an ideal gas are placed in a container whose volume is 8.2 x 103 m3. The absolute pressure of the gas is 4.9 x 10° Pa. What is the average translational kinetic energy of a molecule of the gas? Number Units
Two moles of an ideal gas are placed in a container whose volume is 8.2 x 103 m3. The absolute pressure of the gas is 4.9 x 10° Pa. What is the average translational kinetic energy of a molecule of the gas? Number Units
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![### Ideal Gas Law and Kinetic Energy Calculation
#### Current Attempt in Progress
**Problem Statement:**
Two moles of an ideal gas are placed in a container with a volume of \(8.2 \times 10^{-3} \, \text{m}^3\). The absolute pressure of the gas is \(4.9 \times 10^5 \, \text{Pa}\). What is the average translational kinetic energy of a molecule of the gas?
**Input Fields:**
- **Number:** [ ] (User is expected to input the number value here)
- **Units:** [ ] (User is expected to select the appropriate unit of measurement from a dropdown menu)
**Save for Later** [Button]
---
### Analysis:
To solve for the average translational kinetic energy of a molecule of an ideal gas, we can use the relationship derived from the ideal gas law and the formula for kinetic energy.
**Ideal Gas Law:**
\[ PV = nRT \]
Given:
- \( P = 4.9 \times 10^5 \, \text{Pa} \)
- \( V = 8.2 \times 10^{-3} \, \text{m}^3 \)
- \( n = 2 \, \text{moles} \)
Where:
- \( R \) is the universal gas constant \(8.314 \, \text{J/mol} \cdot \text{K} \)
- \( T \) is the temperature in Kelvins
**Average Translational Kinetic Energy per Molecule:**
\[ E_{\text{avg}} = \frac{3}{2} kT \]
Where:
- \( k \) is Boltzmann's constant \(1.38 \times 10^{-23} \, \text{J/K} \)
By finding the temperature \( T \) from the ideal gas law, we can plug in the value into the equation to find \( E_{\text{avg}} \).
Use the above information and calculations to determine the solution.
*Note:* This explanation is designed to help students understand how to approach and solve the given problem using physics and chemistry concepts related to ideal gases.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae8e54ba-1f6b-4893-86be-39fa86527c96%2F5ed4da65-52e7-4048-9664-3aebd59f8b6b%2F3va087a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Ideal Gas Law and Kinetic Energy Calculation
#### Current Attempt in Progress
**Problem Statement:**
Two moles of an ideal gas are placed in a container with a volume of \(8.2 \times 10^{-3} \, \text{m}^3\). The absolute pressure of the gas is \(4.9 \times 10^5 \, \text{Pa}\). What is the average translational kinetic energy of a molecule of the gas?
**Input Fields:**
- **Number:** [ ] (User is expected to input the number value here)
- **Units:** [ ] (User is expected to select the appropriate unit of measurement from a dropdown menu)
**Save for Later** [Button]
---
### Analysis:
To solve for the average translational kinetic energy of a molecule of an ideal gas, we can use the relationship derived from the ideal gas law and the formula for kinetic energy.
**Ideal Gas Law:**
\[ PV = nRT \]
Given:
- \( P = 4.9 \times 10^5 \, \text{Pa} \)
- \( V = 8.2 \times 10^{-3} \, \text{m}^3 \)
- \( n = 2 \, \text{moles} \)
Where:
- \( R \) is the universal gas constant \(8.314 \, \text{J/mol} \cdot \text{K} \)
- \( T \) is the temperature in Kelvins
**Average Translational Kinetic Energy per Molecule:**
\[ E_{\text{avg}} = \frac{3}{2} kT \]
Where:
- \( k \) is Boltzmann's constant \(1.38 \times 10^{-23} \, \text{J/K} \)
By finding the temperature \( T \) from the ideal gas law, we can plug in the value into the equation to find \( E_{\text{avg}} \).
Use the above information and calculations to determine the solution.
*Note:* This explanation is designed to help students understand how to approach and solve the given problem using physics and chemistry concepts related to ideal gases.
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